One of the main goals of any practical communication system is to capitalize on the available communication resources such as available power, energy, frequency spectrum (bandwidth), time for transmission, and/or cost and size of communication system circuitry. Accordingly, due to the cost, physical limitation of electronic circuitry, government/standard restrictions and the behaviour of communication channels, actual communication systems have strict bandwidth constraints and hence it becomes crucial to maximally utilize the available bandwidth or power given other resources available to the designer. One commonly used measure for bandwidth utilization in practical communication systems is called spectral efficiency, which is defined as a rate of information transfer per time and bandwidth unit (e.g., bits per second per Hertz).
Current state of the art communications systems are designed to transmit digital data over continuous-time channels, see for example Proakis in “Digital Communications” (McGraw Hill, 2001) where a sequence of blocks of modulation values for transmission over a continuous band limited channel, for example X=[x[0], x[1], . . . , x[N−1]], are modulated by a Modulator Unit 110 within the transmitter (not shown for clarity) using a modulation pulse shape s(t) to form a continuous time signal v(t) as given by Equation (1). This continuous time signal is passed over a channel, which is represented in as Channel 150, which introduces additive white Gaussian noise (AWGN), n(t), with a double-sided power spectral density N0/2, to yield received signal {tilde over (c)}(t). At the receiver (not shown for clarity) a De-Modulator Unit 160 demodulates the continuous time signal, for example by sampling a matched filter forming part of the receiver at intervals T yielding a sequence of blocks of demodulated data Y=[y[0], y[1], . . . , y[N−1]] which can be expressed by Equation (2) where s(t) denotes the complex conjugate of s(t) in the case of complex signals.
                              v          ⁡                      (            t            )                          =                              ∑                          n              =              0                                      N              -              1                                ⁢                                    x              ⁡                              [                n                ]                                      ⁢                                          s                ⁡                                  (                                      t                    -                    nT                                    )                                            .                                                          (        1        )                                          y          ⁡                      [            n            ]                          =                  ∫                                    v              ⁡                              (                t                )                                      ⁢                                          s                _                            ⁡                              (                                  t                  -                  nT                                )                                      ⁢                          ⅆ              t                                                          (        2        )            
As depicted in FIG. 1, each of the Modulator Unit 110 and De-Modulator Unit 160 receive modulation pulse shape s(t) and timing T as inputs. Generally, communications systems make use of symmetric, unit normalized energy modulation pulses, ∥s(t)∥2=∫−∞|s(t)|2=1, designed to reduce interference from adjacent modulation values, commonly referred to as InterSymbol Interference (ISI), by keeping ∫−∞∞s(t−iT)s(t−jT)dT for i≠j equal or close to zero for any integers i and j. Further, the shape of the modulation pulses s(t) is generally chosen to Limit or Concentrate the Spectral Energy in a Frequency Range f ε [−½ T,½ T]. Accordingly, transmitting data at intervals T using pulse shapes with total bandwidth f0, e.g. f ε [−f0, f0], is generally referred to as signaling at the Nyquist rate and traditionally represented the upper bound for signaling rate across bandwidth limited channels affected by noise.
Accordingly, within the prior art increasing effective transmission rates from a transmitter to a receiver has focused to avoiding ISI from the transmitter by using a set of orthogonal modulating signals, s(t), s(t−T), . . . , s(t−nT), which may then be temporally and/or frequency overlapped, as long as the inner products of these signals remain zero, i.e. ∫−∞s(t−iT)s(t−jT)dt=0 for any i≠j. Such techniques include, but are not limited to, Orthogonal Frequency Division Multiplexing (OFDM) within telecommunications allowing a large number of closely spaced orthogonal sub-carrier signals to be used to carry data on several parallel data streams or channels whilst each sub-carrier is modulated with a conventional modulation scheme such as quadrature amplitude modulation (QAM) or phase-shift keying (PSK) at a lower symbol rate. Such techniques currently dominate telecommunication networks including for example those relating to digital television and audio broadcasting, DSL broadband internet access, wireless networks, fiber-optic communications, free-space optical communications, Wi-Fi, and fourth generation “4G” mobile communications.
Accordingly, given the demands on such communications systems with evolving connectivity of users, evolving demands from static to dynamic content, and reducing cost expectations, it would be beneficial to further increase network throughput and increase network utilization. Hence, within the prior art, many techniques have been reported by telecommunications systems providers, original equipment manufacturers, and service providers. One such approach is the so-called “water-filling” algorithm for systems design and equalization strategies on communications channels. In the latter scenario, shaping of the transmission spectrum is undertaken to allocate increased power to channels with higher signal-to-noise ratios (SNR) in order to enhance capacity on these imperfect channels such as frequency-selective or ISI channels, multiple-input-multiple-output (MIMO) channels, or multiple-access channels.
Within many current communication systems therefore, such as cellular systems for example, significant bottlenecks are being or have been reached in the spectral efficiency achieved and users supported. Whitespace devices, Long Term Evolution (LTE), femtocells, automatic Wi-Fi handover, and optimized backhaul networks, are just some of the wide range of techniques being exploited to speed the flow of data to wireless devices by wireless operators. However, such techniques ultimately result in base stations and wireless access points that support a maximum number of users at a predetermined maximum data rate established by the appropriate standard against which the infrastructure has been implemented. For example, an LTE cell supports only 200 users per 5 MHz at approximately 10 Mb/s average downlink speed which given the number of users in typical urban environments can be seen to require a large number of cells, e.g. femtocells and picocells, and result in poor connectivity, dropped handovers, etc.
Recently, non-orthogonal signaling methods have been receiving some attention primarily as the result of revived interest in multi-carrier communications. For example, Kozek et al in “Non-Orthogonal Pulseshapes for Multicarrier Communications in Doubly Dispersive Channels” (IEEE J. Sel. Areas Comms., Vol. 16, pp. 1579-1589) showed that non-orthogonal signaling provides for reduced distortions on dispersive channels, i.e., increasing the channel-induced ISI performance. However, restricted only to Riesz based non-orthogonal functions, the reported performance on AWGN channels was still limited to that defined above. Additionally, some signaling schemes such as “Faster than Nyquist” (FTN) within the prior art signaling controlled ISI is known to be beneficial in shaping the spectrum of the transmitted signal and/or simplifying the signal processing at the transmitter/receiver. In FTN signaling, see for example Mazo in “Faster-than-Nyquist Signaling” (Bell Sys. Tech. J., Vol. 54, pp. 1451-1462) the objective is to increase the signaling rate slightly beyond the Nyquist rate without suffering any loss in minimum Euclidean distance between symbols.
Accordingly, it would be beneficial for such wireless networks to support variable allocations such that smaller and smaller frequency sub-bands are allocated to active users, as their number increases, but the individual users/nodes may insert more data-carrying signals in order to compensate for the loss of operating bandwidth arising from the accommodation of more users. It would also be beneficial for an active user within a network supporting a predetermined number of channels may dynamically access additional channels to support data transmission loading. It would further be beneficial for transmitters and receivers according to embodiments of such a network architecture to be based upon low cost design methodologies allowing their deployment within a wide range of applications including high volume, low cost consumer electronics for example.
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying Figures.